Simplify ( square root of 21x^12)/( square root of 3x^3)

$\frac{\sqrt{21 x^{12}}}{\sqrt{3 x^{3}}}$

Combine $\sqrt{21 x^{12}}$ and $\sqrt{3 x^{3}}$ into a single radical.

$\sqrt{\frac{21 x^{12}}{3 x^{3}}}$

Reduce the expression $\frac{21 x^{12}}{3 x^{3}}$ by cancelling the common factors.

Factor $3$ out of $21 x^{12}$ .

$\sqrt{\frac{3 (7 x^{12})}{3 x^{3}}}$

Factor $3$ out of $3 x^{3}$ .

$\sqrt{\frac{3 (7 x^{12})}{3 (x^{3})}}$

Cancel the common factor.

$\sqrt{\frac{3 (7 x^{12})}{3 x^{3}}}$

Rewrite the expression.

$\sqrt{\frac{7 x^{12}}{x^{3}}}$

Cancel the common factor of $x^{12}$ and $x^{3}$ .

Factor $x^{3}$ out of $7 x^{12}$ .

$\sqrt{\frac{x^{3} (7 x^{9})}{x^{3}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{3} (7 x^{9})}{x^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{3} (7 x^{9})}{x^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{7 x^{9}}{1}}$

Divide $7 x^{9}$ by $1$ .

$\sqrt{7 x^{9}}$

Rewrite $7 x^{9}$ as ${({(x^{2})}^{2})}^{2} \cdot (7 x)$ .

Factor out $x^{8}$ .

$\sqrt{7 (x^{8} x)}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{7 ({(x^{4})}^{2} x)}$

Reorder $7$ and ${(x^{4})}^{2}$ .

$\sqrt{{(x^{4})}^{2} \cdot 7 x}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{{({(x^{2})}^{2})}^{2} \cdot 7 x}$

Add parentheses.

$\sqrt{{({(x^{2})}^{2})}^{2} \cdot (7 x)}$

Pull terms out from under the radical.

${(x^{2})}^{2} \sqrt{7 x}$

Multiply the exponents in ${(x^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{2 \cdot 2} \sqrt{7 x}$

Multiply $2$ by $2$ .

$x^{4} \sqrt{7 x}$